International Journal of Mathematics and Mathematical Sciences 
Volume 2004 (2004), Issue 40, Pages 2123-2131
doi:10.1155/S0161171204308227

The axisymmetric Boussinesq-type problem for a half-space under optimal heating of arbitrary profile

J. Rokne,1 B. M. Singh,2 R. S. Dhaliwal,2 and J. Vrbik3

 1Department of Computer Science, University of Calgary, Calgary T2N 1N4, Alberta, Canada
2Department of Mathematics and Statistics, University of Calgary, Calgary T2N 1N4, Alberta, Canada
3Department of Mathematics, Brock University, St. Catharines L2S 3A1, Ontario, Canada
Received 25 August 2003

Abstract

A solution of the axisymmetric Boussinesq-type problem is derived for transient thermal stresses in a half-space under heating by using the Laplace and Hankel transforms. An analytical method is developed to predict the temperature field that satisfies the prescribed mechanical conditions. Several simple shapes of punches of arbitrary profile are considered and an expression for the total load is derived to achieve penetration. The numerical results for the temperature and the total load on the punch are shown graphically.